Assembler Language Assembler Language "Boot Camp""Boot Camp"

Part 1 - Numbers and Part 1 - Numbers and Basic ArithmeticBasic Arithmetic

SHARE 117 in OrlandoSHARE 117 in OrlandoSession 9210Session 9210

August 8, 2011August 8, 2011

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IntroductionIntroduction

Who are we?

John Ehrman, IBM Software Group

Dan Greiner, IBM Systems & Technology Group

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IntroductionIntroduction

Who are you?An applications programmer who needs to write something in mainframe assembler?An applications programmer who wants to understand z/Architecture so as to better understand how HLL programs work?A manager who needs to have a general understanding of assembler?

Our goal is to provide for professionals an introduction to the z/Architecture assembler language

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IntroductionIntroduction

These sessions are based on notes from a course in assembler language at Northern Illinois University

The notes are in turn based on the textbook, Assembler Language with ASSIST and ASSIST/I by Ross A Overbeek and W E Singletary, Fourth Edition, published by Macmillan

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IntroductionIntroduction

The original ASSIST (Assembler System for Student Instruction and Systems Teaching) was written by John Mashey at Penn State University

ASSIST/I, the PC version of ASSIST, was written by Bob Baker, Terry Disz and John McCharen at Northern Illinois University

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IntroductionIntroductionBoth ASSIST and ASSIST/I are in the public domain, and are compatible with the System/370 architecture of about 1975 (fine for beginners)

Everything we discuss here works the same in z/Architecture

Both ASSIST and ASSIST/I are available at http://www.kcats.org/assist

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IntroductionIntroduction

ASSIST-V is also available now, athttp://www.kcats.org/assist-v

Other materials described in these sessions can be found at the same site, at http://www.kcats.org/share

Please keep in mind that ASSIST, ASSIST/I, and ASSIST-V are not supported by Penn State, NIU, or any of us

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IntroductionIntroduction

Other references used in the course at NIU:Principles of Operation (PoO)System/370 Reference SummaryHigh Level Assembler Language Reference

Access to PoO and HLASM Ref is normally online at the IBM publications web site

Students use the S/370 "green card" booklet all the time, including during examinations (SA22-7209)

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Our Agenda for the WeekOur Agenda for the WeekAssembler Boot Camp (ABC) Part 1: Numbers and Basic Arithmetic (Monday - 9:30 a.m.)

ABC Part 2: Instructions and Addressing (Monday - 1:30 p.m.)

ABC Part 3: Assembly and Execution; Branching (Tuesday - 9:30 a.m.)

ABC Lab 1: Hands-On Assembler Lab Using ASSIST/I (Tuesday - 6:00 p.m.)

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Our Agenda for the WeekOur Agenda for the WeekABC Part 4: Program Structures; Arithmetic (Wednesday - 9:30 a.m.)

ABC Lab 2: Hands-On Assembler Lab Using ASSIST/I (Wednesday - 6:00 p.m.)

ABC Part 5: Decimal and Logical Instructions (Thursday - 9:30 a.m.)

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Agenda for this SessionAgenda for this Session

Decimal, Binary and Hexadecimal Numbers and Conversions

Main Storage Organization and Signed Binary Numbers

Integer Arithmetic and Overflow

Getting Started with ASSIST/I

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The Big Question:The Big Question:"Why Learn Assembler "Why Learn Assembler Language?"Language?""People who are more than casually interested in computers should have at least some idea of what the underlying hardware is like. Otherwise the programs they write will be pretty weird."

Donald E Knuth, The Art of Computer Programming, Preface to Fascicle Number One (MMIX)

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Decimal, Binary and Decimal, Binary and Hexadecimal Numbers Hexadecimal Numbers

and Conversionsand Conversions

In Which We Learn to Count In Which We Learn to CountAll Over Again All Over Again

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Why Bother with Binary?Why Bother with Binary?

Nearly all computers today use binary as the internal "language"

We need to understand this language to fully understand instructions and dataEven decimal numbers are represented internally in binary!

Binary numbers can get very long, so we use hexadecimal ("hex") as a shorthand

A hex digit is simply a group of four binary digits (bits)

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Counting in Bases 10, 2, and 16Counting in Bases 10, 2, and 16Dec Bin Hex0 0000 01 0001 12 0010 23 0011 34 0100 45 0101 56 0110 67 0111 7

Dec Bin Hex8 1000 89 1001 910 1010 A11 1011 B12 1100 C13 1101 D14 1110 E15 1111 F16 10000 10

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Numbers in Different BasesNumbers in Different Bases

Consider how we write numbers in base 10, using the digits 0 - 9:

83210 = 80010 + 3010 + 210 = 8 x 102 + 3 x 101 + 2 x 100

For numbers in base 2 we need only 0 and 1:11012 = 10002 + 1002 + 00 + 1 = 1 x 23 + 1 x 22 + 0 x 21 + 1 x 20

But because it requires less writing, we usually prefer base 16 to base 2

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Caution!Caution!

The value of a number may be ambiguous when the base isn't indicated

1011 = ?1010112 = 1110101116 = 411310

The base will usually be clear from the context, but will otherwise be provided

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Converting Binary & Hexadecimal Converting Binary & Hexadecimal to Decimalto Decimal10112 = 1 x 23 = 1 x 8 = 8

+ 0 x 22 = 0 x 4 = 0 + 1 x 21 = 1 x 2 = 2+ 1 x 20 = 1 x 1 = 1 11

A6116 = 10 x 162 = 10 x 256 = 2560 + 6 x 161 = 6 x 16 = 96 + 1 x 160 = 1 x 1 = 1 2657

Note: numbers without subscript are base 10 18

Converting Decimal to Binary & Converting Decimal to Binary & HexadecimalHexadecimal

To convert a decimal number n to base b1. Divide n by b, giving quotient q and remainder r2. Write r as the rightmost digit, or as the digit to

the left of the last one written3. If q is zero, stop; otherwise set n = q and go

back to Step 1.

Note that each digit will be in the range 0 to b-1

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Example: Convert 123Example: Convert 1231010 to Base 16to Base 16

123 / 16 = 7 with remainder 11, so the rightmost digit is B (why?)

7 / 16 = 0 with remainder 7, so the next digit to the left is 7

Since quotient is 0, stop

Result is 12310 = 7B16

A similar process shows 12310 = 1111011220

Conversions Between Bin and HexConversions Between Bin and HexThese are the easiest of the conversions, since 16 = 24 and we can convert by groups of digits

To convert from binary to hexadecimal1. Starting at the right, separate the digits into

groups of four, adding any needed zeros to the left of the leftmost digit so that all groups have four digits

2. Convert each group of four binary digits to a hexadecimal digit

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Conversions Between Bin and HexConversions Between Bin and Hex

So to convert 101101 to hex,1. Group the digits and add zeros: 0010 11012. Convert to hex digits: 2 D

To convert from hexadecimal to binary, simply reverse the algorithm

So 2C516 = 0010 1100 0101 = 10110001012 2 C 5

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Addition and subtraction of unsigned numbers is performed in hexadecimal and binary just the same as it is in decimal, with carries and borrows

We normally use signed numbers, so we won't dwell on unsigned numbers

Arithmetic with Unsigned NumbersArithmetic with Unsigned Numbers

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Addition Table - Base 2 Addition Table - Base 10

+ 0 1 + 0 1 2 3 4 5 6 7 8 9 ——————— ———————————————————————————————————————— 0 | 0 1 0 | 0 1 2 3 4 5 6 7 8 9 1 | 1 0+c 1 | 1 2 3 4 5 6 7 8 9 0+c 2 | 2 3 4 5 6 7 8 9 0+c 1+c 3 | 3 4 5 6 7 8 9 0+c 1+c 2+c 4 | 4 5 6 7 8 9 0+c 1+c 2+c 3+c 5 | 5 6 7 8 9 0+c 1+c 2+c 3+c 4+c 6 | 6 7 8 9 0+c 1+c 2+c 3+c 4+c 5+c 7 | 7 8 9 0+c 1+c 2+c 3+c 4+c 5+c 6+c 8 | 8 9 0+c 1+c 2+c 3+c 4+c 5+c 6+c 7+c 9 | 9 0+c 1+c 2+c 3+c 4+c 5+c 6+c 7+c 8+c

Arithmetic with Unsigned NumbersArithmetic with Unsigned Numbers

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Addition Tables — Base 16

+ 0 1 2 3 4 5 6 7 8 9 A B C D E F ————————————————————————————————————————————————————————————————— 0 | 0 1 2 3 4 5 6 7 8 9 A B C D E F 1 | 1 2 3 4 5 6 7 8 9 A B C D E F 0+c 2 | 2 3 4 5 6 7 8 9 A B C D E F 0+c 1+c 3 | 3 4 5 6 7 8 9 A B C D E F 0+c 1+c 2+c 4 | 4 5 6 7 8 9 A B C D E F 0+c 1+c 2+c 3+c 5 | 5 6 7 8 9 A B C D E F 0+c 1+c 2+c 3+c 4+c 6 | 6 7 8 9 A B C D E F 0+c 1+c 2+c 3+c 4+c 5+c 7 | 7 8 9 A B C D E F 0+c 1+c 2+c 3+c 4+c 5+c 6+c 8 | 8 9 A B C D E F 0+c 1+c 2+c 3+c 4+c 5+c 6+c 7+c 9 | 9 A B C D E F 0+c 1+c 2+c 3+c 4+c 5+c 6+c 7+c 8+c A | A B C D E F 0+c 1+c 2+c 3+c 4+c 5+c 6+c 7+c 8+c 9+c B | B C D E F 0+c 1+c 2+c 3+c 4+c 5+c 6+c 7+c 8+c 9+c A+c C | C D E F 0+c 1+c 2+c 3+c 4+c 5+c 6+c 7+c 8+c 9+c A+c B+c D | D E F 0+c 1+c 2+c 3+c 4+c 5+c 6+c 7+c 8+c 9+c A+c B+c C+c E | E F 0+c 1+c 2+c 3+c 4+c 5+c 6+c 7+c 8+c 9+c A+c B+c C+c D+c F | F 0+c 1+c 2+c 3+c 4+c 5+c 6+c 7+c 8+c 9+c A+c B+c C+c D+c E+c

Arithmetic with Unsigned NumbersArithmetic with Unsigned Numbers

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1101

Main Storage Main Storage Organization and Organization and

Signed Binary NumbersSigned Binary Numbers

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Main Storage OrganizationMain Storage OrganizationIn order to understand how signed numbers are represented in a binary computer, we need to understand memory organization

Abstractly, a binary digit (or bit) can be represented by any 2-state system: on-off, true-false, etc.

A computer's memory is simply a collection of billions of such systems implemented using electronic switches

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Main Storage OrganizationMain Storage OrganizationMemory is organized by grouping eight bits into a byte, then assigning each byte its own identifying number, or address, starting with zero

Bytes are then aggregated into words (4 bytes), halfwords (2 bytes) and doublewords (8 bytes)

One byte = eight bitsOne word = four bytes = 32 bits

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Main Storage OrganizationMain Storage OrganizationTypically, each of these aggregates is aligned on an address boundary which is evenly divisible by its size in bytes

So, a word (32 bits) is aligned on a 4-byte boundary (addresses 0, 4, 8, 12, 16, 20, etc.)

Remember, memory addresses refer to bytes, not bits or words

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Representation of Signed Binary Representation of Signed Binary IntegersIntegers

Representing unsigned binary integers was fairly simple, but how can we include a sign?

There are three ways we might represent signed integers, using a single bit as the sign (customarily the leftmost bit)

Signed-magnitudeOnes' complementTwo's complement

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Representation of Signed Binary Representation of Signed Binary IntegersIntegers

Signed-magnitude is the most familiar (+17, -391) and we will see later how this is used in z/Architecture

Allocating an extra bit for the sign, since 910 = 10012, we would write

+9 as 0 10012 and -9 as 1 10012

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Representation of Signed Binary Representation of Signed Binary IntegersIntegers

The ones' complement of a number is found by replacing each 1 with 0 and each 0 with 1

If we use one bit for the sign, then since 910 is 10012, we would write

+9 as 0 10012 and -9 as 1 01102

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Representation of Signed Binary Representation of Signed Binary IntegersIntegers

The two's complement representation is formed by taking the ones' complement and adding 1

In this notation, again using one bit for the sign, we write

+9 as 0 10012 and -9 as 1 01112

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Representation of Signed Binary Representation of Signed Binary IntegersIntegers

In z/Architecture, a negative binary integer is represented by the two's complement of its positive value

Note that zero is its own complement in this representation (no +0 or -0), since:Zero = 00000000 00000000 00000000 000000001s Comp. = 11111111 11111111 11111111 11111111 Plus 1 = 1Result = 00000000 00000000 00000000 00000000

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Representation of Signed Binary Representation of Signed Binary IntegersIntegers

In a 32- bit word, signed integers are represented by using the first bit as a sign, followed by 31 bits of significance

sbbbbbbb bbbbbbbb bbbbbbbb bbbbbbbb

It is also possible to have signed integers represented as 8-bit bytes and 16-bit halfwords as well as 64-bit doublewords

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Representation of Signed Binary Representation of Signed Binary IntegersIntegers

A word can contain non-negative integers (with sign bit = 0) in the range 0 +231-1 Negative integers (with sign bit = 1) in the range -231+1 -1 are formed by taking the two's complement of the number's absolute value

Negative integer -231 is represented by 1000...0000 or, in hex, 80000000

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Representation of Signed Binary Representation of Signed Binary Integers: ExamplesIntegers: Examples

N.B. -231 is not the two's complement of any positive integer

In two's complement representation +1 = 00000000 00000000 00000000 00000001 -1 = 11111111 11111111 11111111 11111111

Or, in the more commonly used hexadecimal +1 = 00000001 -1 = FFFFFFFF

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Integer Arithmetic Integer Arithmetic and Overflowand Overflow

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Let's look at examples of addition and subtraction using signed numbers in two's complement. These examples use only 4 bits, not 32, with the leftmost bit as sign.+3 = 0 011+2 = 0 010+5 0 101

+3 = 0 011-2 = 1 110 (Two's complement of 0 010)+1 0 001 (The carry out is ignored)

Arithmetic with Signed NumbersArithmetic with Signed Numbers

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Arithmetic with Signed NumbersArithmetic with Signed Numbers

Now, how about -3 plus +2

Notice that the sign is correct each time, and the result is in two's complement notation

-3 = 1 101 +2 = 0 010 -1 1 111

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Arithmetic with Signed NumbersArithmetic with Signed Numbers

Subtraction is performed by adding the two's complement of the subtrahend to the minuend. So +3 - +2 = +3 + (-2).

+3 +3

Computer arithmetic using 32-bit words is a bit more complex, and is always shown in hex. Also, we will no longer display a separate sign bit (it will be part of the leftmost hex digit):

00000011 AE223464 (what sign?) +0000010B +5FCA5243 0000011C 0DEC86A7

Arithmetic with Signed NumbersArithmetic with Signed Numbers

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Subtraction is performed by adding the two's complement

Carries out of the sign position are ignored (results are correct anyway)

F89ABCDE F89ABCDE -6D4AFBC0 = +92B50440 8B4FC11E (is this correct?)

Arithmetic with Signed NumbersArithmetic with Signed Numbers

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Overflow - Why Worry?Overflow - Why Worry?

Internal data is limited in sizeAdding two big numbers can produce a number that is "too big" - then what?

The machine records an overflow conditionEither the Condition Code (CC) is set (more on this later) or a Program Interrupt occursThe result often has the wrong sign

Your programs will probably have to take steps to avoid or handle overflow

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OverflowOverflowWhat if two large numbers are added and the result is greater than 231-1 (or less than -231)?And how can we tell if this happened?

In order to understand this, we will again demonstrate with our very small "words" of four bits, the first of which is the sign

These "4-bit words" can handle integers in the range from -8 to +7 (1 000 to 0 111)

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OverflowOverflowNow let's see what happens when we try to add +5 to +4 (we'll do this in binary, using our four-bit words).

Overflow will occur since the result is greater than +7.

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OverflowOverflowOverflow is detected by checking the carry into the sign position and the carry out of the sign position

If they are not equal, overflow occurred and the result is invalid.

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Out In [not equal, so overflow occurred] \ / 01 00

OverflowOverflow

But be very careful! The mainframe is a binary computer, not hexadecimal, so the check for overflow must be done using the binary representation - that is, we must look at bits, not hex digits

So, if we add as follows... 1111... D13BCF24 D = 1101... +F3C12B97 F = 1111... 1100...

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OverflowOverflow

... we can see that overflow does not occur (1 in and 1 out)

But if we make the mistake of checking the hex digits, we see what looks like overflow

10 D1... +F3...

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Getting Started With Getting Started With ASSIST/IASSIST/I

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ASSIST/I FeaturesASSIST/I Features

ASSIST/I is an integrated assembler and instruction interpreter, plus a text editor and interactive debugger

There are built-in functions (X-instructions) for I/O and data conversion

Program tracing lets you watch "everything" happen

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ASSIST/I FeaturesASSIST/I FeaturesIt is a useful tool for getting started and "tinkering" on a PC without needing any host-system access

A User Guide is included in the "Starter Kit" handout

And it's free!

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ASSIST/I LimitationsASSIST/I Limitations

ASSIST/I supports only an older, less-rich instruction set

Modern assembler features are missing

Programming style may be less robust than desired

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ASSIST/I LimitationsASSIST/I LimitationsText editor functions are rather awkward

It may be easier to use a simple PC editor such as Notepad

System macros aren't available

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Getting Started with ASSIST/IGetting Started with ASSIST/IEasiest: run everything from the CD or hard drive

Change your disk drive to D: (or other appropriate drive letter) and your working directory to \BootAsst\Enter CAS, and follow the prompts to run program DEMOA.ASMLater, we'll step through its execution and show how to create a .PRT file

Try some of the other DEMO programs57